Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

What is the equation of the line that is perpendicular to and has the same y-intercept as the given line?

Given line: [tex]\( y = \frac{1}{5}x + 1 \)[/tex]

A. [tex]\( y = \frac{1}{5}x + 5 \)[/tex]
B. [tex]\( y = 5x + 1 \)[/tex]
C. [tex]\( y = 5x + 5 \)[/tex]

Sagot :

GinnyAnswer
To determine the equation of a line that is perpendicular to a given line and has the same [tex]\( y \)[/tex]-intercept, follow these steps:

### Step 1: Identify the slope of the given line
The given lines are:
1. [tex]\( y = \frac{1}{5}x + 1 \)[/tex]
2. [tex]\( y = \frac{1}{5}x + 5 \)[/tex]
3. [tex]\( y = 5x + 1 \)[/tex]
4. [tex]\( y = 5x + 5 \)[/tex]

We need to work with the first equation, [tex]\( y = \frac{1}{5}x + 1 \)[/tex], to find the slope and [tex]\( y \)[/tex]-intercept of the perpendicular line.

### Step 2: Determine the slope of the perpendicular line
The slope of the given line [tex]\( y = \frac{1}{5}x + 1 \)[/tex] is [tex]\( \frac{1}{5} \)[/tex].

The slope of a line perpendicular to another is the negative reciprocal of the original line's slope. The negative reciprocal of [tex]\( \frac{1}{5} \)[/tex] is [tex]\( -5 \)[/tex].

### Step 3: Determine the [tex]\( y \)[/tex]-intercept of the perpendicular line
The [tex]\( y \)[/tex]-intercept of our given line is [tex]\( 1 \)[/tex]. Since we want the perpendicular line to have the same [tex]\( y \)[/tex]-intercept, we use [tex]\( 1 \)[/tex] as the [tex]\( y \)[/tex]-intercept for the perpendicular line as well.

### Step 4: Write the equation of the perpendicular line
We now have the slope [tex]\( -5 \)[/tex] and the [tex]\( y \)[/tex]-intercept [tex]\( 1 \)[/tex]. Plugging these values into the slope-intercept form [tex]\( y = mx + b \)[/tex], we get:
[tex]\[ y = -5x + 1 \][/tex]

### Conclusion
The equation of the line that is perpendicular to [tex]\( y = \frac{1}{5} x + 1 \)[/tex] and has the same [tex]\( y \)[/tex]-intercept is:
[tex]\[ y = -5x + 1 \][/tex]

Thus, the correct answer is:
[tex]\[ y = -5x + 1 \][/tex]
However, it looks like this form doesn't directly appear in the original options.

Since it is required to choose the corresponding correct option from given options:
The correct line that is perpendicular to the given one and has the correct [tex]\( y \)[/tex]-intercept is indeed not among the provided choices, possibly it needs to be verified as the intended correct perpendicular line equation here is:
[tex]\[ y = -5x + 1 \][/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.